On quantitativeness of diffraction-limited quantitative phase imaging

Differential phase contrast (DPC) is a non-interferometric quantitative phase imaging method achieved by using an asymmetric imaging procedure. We report a pupil modulation differential phase contrast (PMDPC) imaging method by filtering a sample's Fourier domain with half-circle pupils. A phase gradient image is captured with each half-circle pupil, and a quantitative high resolution phase image is obtained after a deconvolution process with a minimum of two phase gradient images. Here, we introduce PMDPC quantitative phase image reconstruction algorithm and realize it experimentally in a 4f system with an SLM placed at the pupil plane. In our current experimental setup with the numerical aperture of 0.36, we obtain a quantitative phase image with a resolution of 1.73μm after computationally removing system aberrations and refocusing. We also extend the depth of field digitally by 20 times to ±50μm with a resolution of 1.76μm.

Hybrid Random Walk-Linear Discriminant Analysis Method for Unwrapping Quantitative Phase Images of Biological Samples

Dielectric metasurfaces have recently attracted much attention due to their ability to efficiently control light propagation, that is, its amplitude, phase and polarization, on micro- and macro- levels. Such metasurfaces also naturally allow for integration in compact optical setups due to their small sizes. An important issue of energy losses is also addressed by employing all-dielectric platform. Advancements in nanofabrication have enabled realization of metasurface-based high-resolution wavefront engineering devices, which have been employed in different imaging applications, for example, as metalenses, polarization filters, metaholograms, etc. Quantitative phase imaging is a powerful tool for the optical inspection of transparent samples in connection with biological and technical applications. By measuring thickness and/or refractive index profiles, phase imaging facilitates, for example, the observation of dynamic events in unstained cells. As such, it has become indispensable in biological imaging, wavefront correction and metrology. However, conventional cameras and photodetectors are inherently not sensitive to the phase of an incident lightwave. As a consequence, direct phase detection is challenging. Only by multiple intensity measurements or application of specialized interferometric schemes, the phase profile of an object can be in principle reconstructed. In this paper, we report on the ability of metasurfaces to contribute to quantitative phase imaging by independent control of the phase profiles in two orthogonal polarization states of an incident beam.

Microscopy combined with the transport of intensity equation is capable of retrieving both intensity and phase distributions of samples from both in-focus and defocus intensities. However, during measurements, the focal plane is often decided artificially and the improper choice may induce errors in quantitative intensity and phase retrieval. In order to obtain accurate in-focus information, quantitative intensity and phase imaging with the numerical focusing transport of intensity equation method combined with cellular duty ratio criterion and numerical wavefront propagation is introduced in this paper. Both numerical simulations and experimental measurements are provided proving this designed method can increase both retrieved in-focus intensity and phase accuracy and reduce dependence of focal plane determination in transport of intensity equation measurements. It is believed that the proposed method can be potentially applied in various fields as in-focus compensation for quantitative phase imaging and automatic focal plane determination, etc.

Quantitative phase imaging provides a way to image transparent objects, such as biological cells, and measure their thickness. We report on a phase-imaging method that achieves twice the phase shift and approximately 1.7 times the spatial resolution of an equivalent spatially and temporally coherent classical quantitative phase-imaging system by using quantum interference between successive spontaneous parametric downconversion events in a nonlinear crystal. Furthermore, our method is approximately 1000 times faster than imaging the parametric downconversion photons in coincidence, which requires measurement times on the order of tens of hours. Our method may be useful for imaging sensitive transparent objects that require low illumination intensities at near-infrared and longer illumination wavelengths, such as photosensitive biological samples.

The advantages of quantitative phase microscopy (QPM) such as label-free imaging with high spatial sensitivity, live cell compatibility and high-speed imaging makes it viable for various biological applications. The measurement accuracy of QPM strongly relies on the shape of the recorded interferograms, whether straight or curved fringes are recorded during the data acquisition. Moreover, for a single shot phase recovery high fringe density is required. The wavefront curvature for the high-density fringes over the entire field of view is difficult to be discerned with the naked eye. As a consequence, there is a quadratic phase aberration in the recovered phase images due to curvature mismatch. In the present work, we have implemented sampling moiré method for real-time sensing of the wavefront curvature mismatch between the object and the reference wavefronts and further for its correction. By zooming out the interferogram, moiré fringes are generated which helps to easily identify the curvature of the fringes. The wavefront curvature mismatch correction accuracy of the method is tested with the help of low temporal coherent light source such as a white light (temporal coherence ∼ 1.6 µm). The proposed scheme is successfully demonstrated to remove the quadratic phase aberration caused due to wavefront mismatch from an USAF resolution target and the biological tissue samples. The phase recovery accuracy of the current scheme is further compared with and found to better than the standard method called principle component analysis. The proposed method enables recording of the corrected wavefront interferogram without needing any additional optical components or modification and also does not need any post-processing correction algorithms. The proposed method of curvature compensation paves the path for a high-throughput and accurate quantitative phase imaging.

Quantitative phase microscopy (QPM) is a label-free imaging technique often employed for long-term, high-contrast imaging of live bio-samples. Yet, QPM is not specific to a certain subcellular organelle. As a remedy, fluorescence microscopy can visualize specific subcellular organelles once being labeled with fluorescent markers. In this paper, a high-resolution phase/fluorescence dual-modality microscopic imaging method based on structured light illumination is proposed. In a dual-modality microscopic system, periodic stripes are generated by a digital micromirror array (DMD), and are used as the common illumination for both modalities. For QPM imaging, the holograms of the sample under structured light illuminations from different directions and phase shifts are recorded, from which a quantitative phase image with resolution enhancement can be reconstructed via a synthetic aperture procedure. Furthermore, a numerical approach is proposed to compensate for the environmental disturbances that often challenge aperture synthesis of phase imaging. This method determines each time the phase distortions caused by environmental disturbances through using the spectrum of the 0th order of the structured light illumination, and the phase distortions are removed from the phase distributions of the waves along the 0th and the ±1st diffraction orders. Resolution enhancement of QPM imaging is realized by synthesizing the spectra of all the waves along different diffraction orders of the structured light illuminations of different orientations. With phase images, three-dimensional shapes, inner structures, or refractive index distributions of transparent and translucent samples can be obtained. For fluorescence imaging, intensity images (morie patterns) of the sample under different structured light illuminations are recorded. The spectra along different diffraction orders are separated by using a phase shifting reconstruction algorithm, and are shifted to their original positions, forming a synthesized spectrum that is much broader than the spectra of raw intensity images (NA-limited spectra). An inverse Fourier transform on the synthesized spectrum yields a super-resolution fluorescence image of the sample. With the reconstructed fluorescence images, specific subcellular organelles labeled with fluorescent markers can be visualized. The combination of quantitative phase microscopy and fluorescence microscopy can obtain multidimensional information about the sample. In this dual-mode imaging system, the spatial resolution of quantitative phase imaging and fluorescence imaging are 840 nm and 440 nm, respectively. The proposed dual-mode microscopy imaging technique has been demonstrated for imaging fluorescent beads, fly wings, spring/rice leaves, mouse tail transection, and fluorescence-stained SiHa cells. We envisage that this method can be further applied to many fields, such as biomedicine, industry, and chemistry.

Quantitative phase imaging (QPI) provides enhanced contrast for weakly absorbing specimens such as biological tissues under optical light and soft materials under X-ray. In this work, we develop a model-based phase retrieval framework by integrating the physics principles of phase imaging with the deep learning-based approach. Both measurements and the forward model are used as the inputs for a model-based neural network. The features of the object and the regularization weight of the established priors are learned by minimizing the difference between the network output to the ground truth during the training process. This method is tested on phase imaging of handwriting digital patterns and biological cells in a simulation of propagation-based TIE (transport of intensity equation) phase retrieval. We achieve enhanced accuracy for the phase retrieval compared to non-model based end-to-end neural networks and reduce the computation cost compared to traditional model-based iterative reconstruction algorithms.

Inflammatory bowel diseases (IBD) are inflammatory disorders of the gastrointestinal tract characterized by a chronic relapsing disease course. As uncontrolled intestinal inflammation can result in severe disease complications, recent treatment targets of IBD evolved toward seeking the absence of mucosal and histological inflammation. However, this approach requires adequate histological evaluation of IBD disease activity. The diagnostic challenge of histological examination of intestinal inflammation is documented by the multitude of proposed histological scoring systems. In this context, we review quantitative phase imaging (QPI) techniques such as digital holographic microscopy (DHM) for characterizing intestinal inflammation. DHM determines optical path-length delays in a stain-free manner, thereby providing the tissue refractive index as a biophysical marker that directly correlates to tissue density. Recently, DHM has been successfully applied in cell biology, cancer cell research and infectious-induced cellular alterations. We summarized the capabilities of DHM and related QPI techniques to assess the severity of intestinal inflammation in experimental colitis as well as in colonic samples from human IBD patients. Moreover, we illustrate major advantages of DHM facilitated multimodal evaluation of epithelial wound healing processes as assessed by physical parameters like cell volume, density, thickness and dry mass in vitro. Furthermore, potential limitations of DHM and future utilities of QPI are discussed. In conclusion, DHM represents a promising, easy-to-use quantitative tool to provide accurate and objective assessment of intestinal inflammation and may pave the way towards automated label-free digital pathology and related in vitro cell culture analysis in future.

Transmission optical coherence tomography (tOCT) is gaining interest for imaging biological samples; however, so far, quantitative phase information has not been directly obtained. This study introduces SOPHAST-OCT, an approach for integrated 2D phase recovery in Off-Axis Full-Field Swept-Source tOCT. It uses phase-shifting to leverage OCT’s inherent phase changes between recorded interferograms. SOPHAST-OCT demonstrates promising phase agreement with the simulated ground truth phase. This approach represents a first step toward quantitative imaging in tOCT. Full Text: PDF References Y. Park, C. Depeursinge, G. Popescu, "Quantitative phase imaging in biomedicine", Nature Photon 12, 578 (2018). CrossRef K. Alm, H. Cirenajwis, L. Gisselsson, A.G. Wingren, B. Janicke, A. Mölder, et al., in Holography, Research and Technologies (IntechOpen, 2011). CrossRef W. Drexler, J. Fujimoto, editors , Optical Coherence Tomography: Technology and Applications, 2nd ed. (Springer Cham, 2015). CrossRef W. Krauze, P. Ossowski, M. Nowakowski, M. Szkulmowski, M. Kujawińska, "Enhanced QPI functionality by combining OCT and ODT methods", Quantitative Phase Imaging VII, 11653, 19 (2021). CrossRef B.C. Wilson, S.L. Jacques, "Optical reflectance and transmittance of tissues: principles and applications", IEEE J. Quantum Electron. 26, 2186 (1990). CrossRef J. van der Horst, A.K. Trull, J. Kalkman, "Deep-tissue label-free quantitative optical tomography", Optica 7, 1682 (2020). CrossRef P. Hosseini, Y. Sung, Y. Choi, N. Lue, Z. Yaqoob, P. So, "Scanning color optical tomography (SCOT)", Opt. Expr. 23, 19752 (2015). CrossRef P. de Groot, "Phase Shifting Interferometry" in Optical Measurement of Surface Topography, edited by R. Leach (Springer, Berlin, Heidelberg, 2011). CrossRef M. Wojtkowski, A. Kowalczyk, R. Leitgeb, A.F. Fercher, "Full range complex spectral optical coherence tomography technique in eye imaging", Opt. Lett. 27, 1415 (2002). CrossRef Q. Zhang, S. Zhong, J. Lin, W. Chen, M. Luo, J. Zhong, Y. Yu, Z. Peng, S. Cheng, "Full-range Fourier-domain optical coherence tomography based on Mach–Zehnder interferometer", Opt. Lasers Engin. 124, 105794 (2020). CrossRef R. Juarez-Salazar, C. Robledo-Sanchez, F. Guerrero-Sanchez, A. Rangel-Huerta, "Generalized phase-shifting algorithm for inhomogeneous phase shift and spatio-temporal fringe visibility variation", Opt. Express 22, 4738 (2014). CrossRef R. Juarez-Salazar, C. Robledo-Sánchez, C. Meneses-Fabian, F. Guerrero-Sánchez, L. M. Arévalo Aguilar, "Generalized phase-shifting interferometry by parameter estimation with the least squares method", Opt. Lasers Engin. 51, 626 (2013). CrossRef M.A. Herráez, D.R. Burton, M.J. Lalor, M.A. Gdeisat, "Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path", Appl. Opt. 41, 7437 (2002). CrossRef Z. Wang, A.C. Bovik, "A universal image quality index", IEEE Signal Proc. Lett. 9, 81 (2002). CrossRef

A well-known speckle which comes from the coherent property of laser source has limited the laser imaging application. Quantitative Phase Imaging (QPI) also suffers from this speckle noise when illuminate with coherent source. A rotational diffuser is a considerable method to minimize the speckle by averaging the speckle contrast in time. Here, we employ the dual optical diffuser-static and moving diffusers — to suppress speckle noise in QPI. Continuous-wave laser is used to illuminate polystyrene micro-bead as a sample. Due to the averaging independent speckle pattern, speckle noise in phase image is reduced by maintaining the quality of fringe. The ability of moving diffuser in speckle noise suppression is presented in Fourier domain via Fast Fourier Transform (FFT) technique and topographic phase map. This work proposes a valuable technique for efficient suppression of the coherent speckle in QPI.

Wedge prism assisted quantitative phase imaging on standard microscopes

Quantitative differential phase-contrast (DPC) imaging is one of the commonly used methods for phase retrieval. However, quantitative DPC imaging requires several pairwise intensity measurements, which makes it difficult to monitor living cells in real-time. In this study, we present a single-shot quantitative DPC imaging method based on the combination of deep learning (DL) and color-encoded illumination. Our goal is to train a model that can generate an isotropic quantitative phase image (i.e., target) directly from a single-shot intensity measurement (i.e., input). The target phase image was reconstructed using a linear-gradient pupil with two-axis measurements, and the model input was the measured color intensities obtained from a radially asymmetric color-encoded illumination pattern. The DL-based model was trained, validated, and tested using thirteen different cell lines. The total number of training, validation, and testing images was 264 (10 cells), 10 (1 cell), and 40 (2 cells), respectively. Our results show that the DL-based phase images are visually similar to the ground-truth phase images and have a high structural similarity index (>0.98). Moreover, the phase difference between the ground-truth and DL-based phase images was smaller than 13%. Our study shows the feasibility of using DL to generate quantitative phase imaging from a single-shot intensity measurement.

Quantitative phase measurements at multiple wavelengths has created an opportunity for exploring new avenues in phase microscopy such as enhancing imaging-depth (1), measuring hemoglobin concentrations in erythrocytes (2), and more recently in tomographic mapping of the refractive index of live cells (3). To this end, quantitative phase imaging has been demonstrated both at few selected spectral points as well as with high spectral resolution (4,5). However, most of these developed techniques compromise imaging speed, field of view, or the spectral resolution to perform interferometric measurements at multiple colors. In the specific application of quantitative phase in studying blood diseases and red blood cells, current techniques lack the required sensitivity to quantify biological properties of interest at individual cell level. Recently, we have set out to develop a stable quantitative interferometric microscope allowing for measurements of such properties for red cells without compromising field of view or speed of the measurements. The feasibility of the approach will be initially demonstrated in measuring dispersion curves of known solutions, followed by measuring biological properties of red cells in sickle cell anemia.

Digital holographic microscopy (DHM), which provides quantitative phase imaging (QPI), has been widely applied in material and biological applications. The performance of DHM technologies relies heavily on computational reconstruction methods to provide accurate phase measurements. For example, non-telecentric DHM systems should compensate for the spherical wavefront associated with a non-telecentric configuration. The size of the ±1 diffraction orders in the hologram spectrum depends inversely on the radius of the curvature of the spherical wavefront introduced by the non-telecentric DHM system. Therefore, one can estimate the radius of curvature of the spherical wavefront by analyzing the hologram spectrum. Here, we outline the steps for the automatic reconstruction of phase images without distortions and with minimum user input from a hologram recorded in a non-telecentric DHM system. The proposed reconstruction approach can be divided into six main steps. The first step automatically selects the +1 diffraction order in the hologram spectrum. Secondly, the spherical wavefront parameters and the interference angle are estimated by analyzing the size and position of the selected +1 order. The third and fourth steps are the spatial filtering of the +1 order and the compensation of the interference angle, respectively. The next step involves the estimation of the center of the spherical wavefront. Finally, there is a fine-tuning step to optimize the estimated parameters and provide a phase image with minimum phase distortions. We have identified the relevant metrics in each step, compared multiple approaches, and selected the one with the higher performance for all our experimental holograms.